Cops in Miami and Hollywood, FL, as well as Pittsburgh, PA, tell TMZ Sports they have NO records of Antonio Brown's rape accuser ever filing a criminal complaint with officers.

A woman named Britney Taylor alleges the NFL superstar sexually assaulted her twice in the Pittsburgh area in 2017 ... and claims Brown raped her in the Miami area in 2018.

When we spoke with officials from the Hollywood Police Department in Florida -- where Brown has a residence -- they told us they have no records of a complaint ever filed by Taylor.

A spokesperson from the Department of Public Safety in Pittsburgh says they have no records of a complaint either, adding, there are "no active investigations into" Brown at this time.